Assume (3, 4) is on graph. What is corresponding pt for...?

[destiny_deity]

Assume that the point (3,4) is on the graph of y = f(x). What point is on the graph of the following composites:

1) y= 2f(x)

2) y= 2 + f(x)

Step-by step process is needed.

Also, is it possible to graph it? If so, how do I do it on my TI-86 calculator?

Many thanks to those who replies to this!

 

[jwpaine]

Re: I need help on the following questions.

Assume that the point (3,4) is on the graph of y = f(x). What point is on the graph of the following composites:

y= 2f(x)

y= 2 + f(x)

Step-by step process is needed.

Also, is it possible to graph it? If so, how do I do it on my TI-86 calculator?

Many thanks to those who replies to this!

You have one vertical shift and one non-rigid transformation:

let's make up a function to help explain:

f(x) = x
thus f(x) + 2 = x + 2 giving us a vertical shift up, two units.

The same thing can be done for your non-rigid transformation of 2f(x) = y; then simply plug in the values from your ordered pairs and simplify.

Lets say we have the point (3,8)

f(x) = y
f(3) = 8

thus f(x) + 2 = y + 2 ---> f(3) + 2 = 10 ---> (3,10) for your vertical shift

you can graph this in the form of y=mx+b using your graphing calculator: if you have a TI you can go into the y= window and enter in a value and a transformation and then hit "graph".

Cheers!

 

[destiny_deity]

Thanks very much for your help.